SEA rsfcMRI - Longitudinal Descriptives

Load the data

Starting with the Schaefer 400-parcel, 7 network atlas.

#set variables for `collect_data`
if(fslong){
  fname <- 'sea_rsfc_fslong_schaefer400x7.RDS'
  data_dir <- '/net/holynfs01/srv/export/mclaughlin/share_root/stressdevlab/SEA_REST/derivatives/fmriprep-20.1.1/xcpengine-default/'
  subs <- sprintf('sub-10%02d', c(1:16,18:31))
  sess <- sprintf('%02d', 1:10)
  subses <- expand.grid(sess, subs)
  files <- paste0(data_dir, '/', subses[,2], subses[,1], '/fcon/schaefer400x7/', subses[,2], subses[,1], '_schaefer400x7.net')
  file_id <- paste0(subses[,2], '_', subses[,1])  
} else {
  fname <- 'sea_rsfc_schaefer400x7.RDS'
 data_dir <- '/net/holynfs01/srv/export/mclaughlin/share_root/stressdevlab/SEA_BIDS/derivatives/1.4.1-final/xcpengine-default'
  subs <- sprintf('sub-10%02d', c(1:16,18:31))
  sess <- sprintf('ses-%02d', 1:10)
  subses <- expand.grid(sess, subs)
  files <- paste0(data_dir, '/', subses[,2], '/', subses[,1], '/fcon/schaefer400x7/', subses[,2], '_', subses[,1], '_schaefer400x7.net')
  file_id <- paste0(subses[,2], '_', subses[,1])
}

#This should be easy to generalize
#option to set directory and search path
#option to rad in label file

library(data.table)
library(tidyr)
if(is.na(ncores <- as.numeric(Sys.getenv('SLURM_CPUS_ON_NODE')))){
  ncores <- 10
  message('No environment variable specifying number of cores. Setting to ', ncores, '.')
}
setDTthreads(ncores)

if(file.exists(fname)){
  adt_labels <- readRDS(fname)
  schaefer_400_7_net_ids <- readRDS('schaefer_ids.RDS')
} else {
  message('Creating file list...')
  files_list <- lapply(files, function(x) ifelse(file.exists(x), x, ''))
  
  message('Reading rsfc files...')
  if(ncores > 1){
    message('Using ', ncores, ' cores to read files.')
    cl <- parallel::makePSOCKcluster(max(c(ncores - 1), 1))
    
    adt_list <- unlist(parallel::parLapply(cl = cl, split(files, 1:ncores), function(part){
      lapply(part, function(f){
        if(file.exists(f)){
          data.table::fread(f, skip = 2, col.names = c('node1', 'node2', 'r'))
        } else {
          data.table::data.table()
        }
      })
    }), recursive = FALSE)
    try(parallel::stopCluster(cl))
  } else {
    adt_list <- lapply(files, function(f){
      if(file.exists(f)){
        data.table::fread(f, skip = 2, col.names = c('node1', 'node2', 'r'))
      } else {
        data.table::data.table()
      }
    }) 
  }
  names(adt_list) <- file_id
  
  message('Combining data, assigning labels...')
  adt <- rbindlist(adt_list, idcol = 'id')
  
  #https://github.com/ThomasYeoLab/CBIG/tree/master/stable_projects/brain_parcellation/Schaefer2018_LocalGlobal/Parcellations/MNI
  schaefer_400_7_net_ids <- fread('Schaefer2018_400Parcels_7Networks_order.txt', 
                                  col.names = c('node1', 'network1', 'V1', 'V2', 'V3', 'V4'))
  schaefer_400_7_net_ids[, c('V1', 'V2', 'V3', 'V4') := NULL]
  schaefer_400_7_net_ids <- schaefer_400_7_net_ids %>% 
    tidyr::extract(network1, c('network1', 'roi1'), '7Networks_([RL]H_.*)_(\\d+)')
  
  setkey(adt, node1)
  setkey(schaefer_400_7_net_ids, node1)
  adt_labels1 <- schaefer_400_7_net_ids[adt]
  setnames(schaefer_400_7_net_ids, c('node2', 'network2', 'roi2'))
  setkey(adt_labels1, node2)
  setkey(schaefer_400_7_net_ids, node2)
  adt_labels <- schaefer_400_7_net_ids[adt_labels1]
  adt_labels[, c('id', 'sess') := tstrsplit(id, '_', fixed = TRUE)]
  message('Saving RDS file to: ', fname)
  saveRDS(adt_labels, fname)
  message('Saving Schaefer ID data table to schaefer_ids.rds')
  saveRDS(schaefer_400_7_net_ids, 'schaefer_ids.RDS')
}

if(FALSE){
  adt_labels_old <- readRDS('sea_rsfc_schaefer400x7.RDS')
  missing_files_csv <- data.table(file = files, does_not_exist = files_list == '')
  View(missing_files_csv[does_not_exist == TRUE])
  readr::write_csv(data.table(file = files, does_not_exist = files_list == ''), 
                   '~/sea_rsfc-missing_fcon_output.csv')
  
  a <- data.table(file = files, does_not_exist = files_list == '')
  a[, fcon_missing := lapply(gsub('(.*/fcon)/.*', '\\1', file), function(x) !file.exists(x))]
  a[, missmatch := does_not_exist != fcon_missing ]
  a[(missmatch), file]
}

Retain just within-network connectivity. Also, Fisher-z transform the correlations for analyses. One small detail that is important here is that we keep network connectivity for same-hemisphere parcels only.

sea_schaefer400_7_withinnet <- copy(adt_labels)

sub_regex <- '[LR]H_[A-Za-z]+_*(.*)'
net_regex <- '[LR]H_([A-Za-z]+)_*(?:.*)'
hem_regex <- '([LR]H)_[A-Za-z]+_*(?:.*)'
sea_schaefer400_7_withinnet_nets <- distinct(sea_schaefer400_7_withinnet, network1)
sea_schaefer400_7_withinnet_nets[, sub1 := gsub(sub_regex, '\\1', network1)]
sea_schaefer400_7_withinnet_nets[, net1 := gsub(net_regex, '\\1', network1)]
sea_schaefer400_7_withinnet_nets[, hem1 := gsub(hem_regex, '\\1', network1)]
setkey(sea_schaefer400_7_withinnet, network1)
setkey(sea_schaefer400_7_withinnet_nets, network1)
sea_schaefer400_7_withinnet <- sea_schaefer400_7_withinnet_nets[sea_schaefer400_7_withinnet]

setnames(sea_schaefer400_7_withinnet_nets, c('network2', 'sub2', 'net2', 'hem2'))
setkey(sea_schaefer400_7_withinnet, network2)
setkey(sea_schaefer400_7_withinnet_nets, network2)
sea_schaefer400_7_withinnet <- sea_schaefer400_7_withinnet_nets[sea_schaefer400_7_withinnet]

sea_schaefer400_7_withinnet <- sea_schaefer400_7_withinnet[net1 == net2 & hem1 == hem2]
sea_schaefer400_7_withinnet[, c('network1', 'network2') := NULL]
sea_schaefer400_7_withinnet[, z := atanh(r)]
sea_schaefer400_7_withinnet[, H := dplyr::case_when(hem1 == 'RH' ~ -1,
                                                    hem1 == 'LH' ~ 1)]
if(!dim(distinct(sea_schaefer400_7_withinnet, net1, net2, hem1, hem2))[[1]] == 14){
  stop('Incorrect number of networks')
}

Check No. of RS Features

Using the number nodes are in each network allows computation of the expected number of rsfc features, which allows a comparison to the observed number of features to find instances where certain connections are missing.

#Check to make sure we're getting the number of connectivity features per network we expect
setkey(sea_schaefer400_7_withinnet_nets, 'network2')
setkey(schaefer_400_7_net_ids, 'network2')

nodes_per_net <- sea_schaefer400_7_withinnet_nets[schaefer_400_7_net_ids][, .N, by = c('net2', 'hem2')]
nodes_per_net[, expected_Nfeatures := N * (N - 1) / 2]

connectivity_feature_check <- sea_schaefer400_7_withinnet[, .(Nfeatures = .N), by = c('net2', 'hem2', 'id', 'sess')][nodes_per_net[, !'N'], on = c('net2', 'hem2')]

setnames(connectivity_feature_check, c('net2', 'hem2'), c('nework', 'hemisphere'))

dt_options <- list(rownames = FALSE,
                   filter = 'top',
                   class = 'cell-border stripe',
                   extensions = 'Buttons', 
                   options = list(dom = 'Bfrtip', buttons = c('csv')))
do.call(DT::datatable, 
        c(list(connectivity_feature_check[Nfeatures != expected_Nfeatures],
               caption = 'Mismatch of observed and expected number of rsfc features'), 
          dt_options))

do.call(DT::datatable, 
        c(list(connectivity_feature_check[Nfeatures != expected_Nfeatures][, .N, by = c('id', 'sess')],
               caption = 'Number of mismatches for subject sessions'),
          dt_options))

Some QC

Density of functional connectivity (pearson correlation) for each participant, for each subject, overlayed on the density for all sessions and participants.

#Generate group-level density
agg_mean <- mean(sea_schaefer400_7_withinnet$z)
agg_sd <- sd(sea_schaefer400_7_withinnet$z)
scalez <- (sea_schaefer400_7_withinnet$z - agg_mean) / agg_sd
density_agg <- density(scalez)
sea_schaefer400_densplot_agg <- data.table(x = density_agg$x,
                                           x_on_z = density_agg$x * agg_sd + agg_mean,
                                           y = density_agg$y)
#Generate per-participant-session densities
sea_schaefer400_MSD <- sea_schaefer400_7_withinnet[, list(mean = mean(z),
                                                          sd = sd(z)), 
                                                   by = c('id', 'sess')]
sea_schaefer400_densplot <- sea_schaefer400_MSD[sea_schaefer400_7_withinnet, 
                                                on = c('id', 'sess')]
sea_schaefer400_densplot[, scalez := (z - mean)/sd]
sea_schaefer400_densplot <- 
  sea_schaefer400_MSD[sea_schaefer400_densplot[, list(x = density(scalez)$x,
                                                      y = density(scalez)$y), 
                                               by = c('id', 'sess')],
                      on = c('id', 'sess')][, x_on_z := sd*x + mean]

u_ids <- unique(sea_schaefer400_densplot$id)
for(an_id in u_ids){
  cat(paste0('\n\n## ', an_id, '\n\n'))
  
  hplot <- ggplot(sea_schaefer400_densplot_agg, aes(x = tanh(x_on_z), y = y)) + 
    geom_ribbon(ymin = 0, aes(ymax = y, fill = 'Group', color  = 'Group'), 
                alpha = .5) + 
    geom_ribbon(data = sea_schaefer400_densplot[id == an_id, ], 
                ymin = 0, aes(ymax = y, fill = 'ID', color  = 'ID'), 
                alpha = .5) + 
    scale_fill_manual(aesthetics = c('color','fill'), breaks = c('Group', 'ID'), labels = c('Group', 'Participant'), values = apal[c(2,4)], name = 'Data') +
    facet_wrap(~sess, ncol = 2) + 
    labs(x = 'correlation', y = 'density') + 
    coord_cartesian(xlim = c(-1, 1), ylim = c(0, .5)) + 
    jftheme
  print(hplot)
}

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Modeling

We are interested in stability and variability for each network. For each participant, we have multiple sessions, and within each session, we have multiple parcel-parcel pairs that provide information about the within-network connectivity. We can use the fact that we have multiple indicators of within-network connectivity to estimate the between-person variability, as well as the within-person (session-to-session) variability as distinct from measurement error (we assume that each parcel-parcel functional connectivity estimate in a network is an estimate of that network's connectivity)^*.

* This assumption means that we essentially treat differences in the FC between one pair and another as measurement error.

We can compute an ICC that describes both within-person and between-person variability by using a 3 level model. First, I subset the data for a single network. I then build an intercept-only model, allowing the intercept to vary by participant-ID, and by session within each ID. The intercept is effectively the mean across all intrahemispheric parcel-pairs.

\[ \begin{align} z &= \beta_{0jk} + \epsilon_{ijk} \\ \beta_{0jk} &= \pi_{00k} + \nu_{0jk} \\ \pi_{00k} &= \gamma_{000} + \upsilon_{00k} \end{align} \]

\[ \begin{align} z = \gamma_{000} + \upsilon_{00k} + \nu_{0jk} + \epsilon_{ijk} \end{align} \] Where \(z\) is the measure of functional connectivity, and \(i\) indexes observations within each session, \(j\), for each participant \(k\). This means that we are able to estimate variance in per-person deviations (\(\upsilon_{00k}\)) from the network mean-connectivity (\(\gamma_{000}\)), per-session-deviations (\(\nu_{0jk}\)) from those per-person deviations, and the residual not explained by variability over persons or person-sessions (\(\epsilon_{ijk}\)).

Testing these out

I want to make sure that these models are correct, so I'll compare the variance portions, and total variance, between the two models.

library(lme4)
networks <- unique(sea_schaefer400_7_withinnet$net1)
this_net <- networks[[2]]
this_net_dt <- sea_schaefer400_7_withinnet[net1 == this_net] 

model_dir <- 'models'
test_model_list <- list(test_2l = list(fn = file.path(model_dir, 'test_noh_2l.RDS'),
                                         form = z ~ 1 + (1 | id)),
                          test_3l = list(fn = file.path(model_dir, 'test_noh_3l.RDS'),
                                         form = z ~ 1 + (1 | id/sess)))
cl <- parallel::makePSOCKcluster(max(c(ncores - 1), 1))

test_model_fits <- parallel::parLapply(cl = cl, test_model_list, function(model_list, d){
  library(lme4)
  if(!file.exists(model_list[['fn']])){
    f <- model_list[['form']]
    fit <- lmer(f, data = d)
    saveRDS(fit, model_list[['fn']])
  } else {
    fit <- readRDS(model_list[['fn']])
  }
  return(fit)
}, d = this_net_dt)

try(parallel::stopCluster(cl))

three_level <- test_model_fits$test_3l

summary(three_level)

## Linear mixed model fit by REML ['lmerMod']
## Formula: z ~ 1 + (1 | id/sess)
##    Data: d
## 
## REML criterion at convergence: 104819.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4411 -0.6836 -0.0859  0.5975  6.1243 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  sess:id  (Intercept) 0.004974 0.07052 
##  id       (Intercept) 0.000000 0.00000 
##  Residual             0.083024 0.28814 
## Number of obs: 298033, groups:  sess:id, 152; id, 30
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) 0.185494   0.005745   32.29
## convergence code: 0
## boundary (singular) fit: see ?isSingular

lll_varcorr <- VarCorr(three_level)

report_df <- data.frame(
  stat = c('id_var', 'sess_var', 'resid_var', 'total_var'),
  three_level = c(lll_varcorr$id.1['(Intercept)','(Intercept)'],
                  lll_varcorr$sess.id.1['(Intercept)','(Intercept)'],
                  sigma(three_level)^2,
                  sum(unlist(lapply(lll_varcorr, diag))) + sigma(three_level)^2))

report_df$three_level_perc <- 
  sprintf('%.1f%%', report_df$three_level/report_df$three_level[[4]]*100)
report_df$three_level_RE_perc <- 
  c(sprintf('%.1f%%', report_df$three_level[1:2]/sum(report_df$three_level[1:2])*100), '-', '-')
knitr::kable(report_df, digits = 5)

stat	three_level	three_level_perc	three_level_RE_perc
id_var	0.08302	94.3%	48.5%
sess_var	0.08800	100.0%	51.5%
resid_var	0.08302	94.3%	-
total_var	0.08800	100.0%	-

Fit for each network

networks <- unique(sea_schaefer400_7_withinnet$net1)

netlist <- lapply(networks, function(this_net){
  return(list(network = this_net, d = sea_schaefer400_7_withinnet[net1 == this_net]))
})

cl <- parallel::makePSOCKcluster(max(c(ncores - 1, 1)))
model_fits <- parallel::parLapply(cl = cl, netlist, function(anet, fslong){
  this_net <- anet[['network']]
  this_net_dt <- anet[['d']]
  model_dir <- 'models'
  fslong_name <- ''
  if(fslong)
    fslong_name <- 'fslong-'
  model_fit_fn <- file.path(model_dir, paste0('lmer_fit-3l-', fslong_name, this_net, '.RDS'))
  library(lme4)
  if(!file.exists(model_fit_fn)){
    fit <- lmer(z ~ 1 + (1 | id/sess), data = this_net_dt)
    saveRDS(fit, model_fit_fn)
  } else {
    fit <- readRDS(model_fit_fn)
  }
  return(fit)
}, fslong = fslong)
try(parallel::stopCluster(cl))

proportion_variance_tables <- lapply(model_fits, function(model_fit){
  vc <- VarCorr(model_fit)
  id_v <- vc$id['(Intercept)','(Intercept)']
  idsess_v <- vc$`sess:id`['(Intercept)','(Intercept)']
  s_2 <- sigma(model_fit)^2
  total_RE <- sum(unlist(lapply(vc, diag)))
  other_RE <- total_RE - id_v - idsess_v
  total <- total_RE + s_2
  rez <- data.frame(source = rep(c('ID', 'ID/Session', 'Other RE', 'Residual'),2),
                    out_of = factor(c(rep('total', 4), rep('RE', 4)), levels = c('total', 'RE')),
                    percent = c(c(id_v, idsess_v, other_RE, s_2)*100 / total,
                                c(id_v, idsess_v, other_RE, NA)*100 / total_RE))
  if(other_RE == 0){
    rez <- rez[rez$source != 'Other RE',]
  }
  return(rez)
})

The plots on the left, below, show model-expected functional connectivity pearson correlations for each participant, for each session, overlayed on the raw data (one point per parcel, per session, per participant). A line for each participant's model-expected mean across all sessions is overlayed on this. The right plot shows proportions of variance accounted for by the random effect estimates as a proportion of both total variance, and total random effects (RE) variance. The total RE variance includes individual means (ID), individual means per session (ID/Session), and the difference in connectivity between right and left hemispheres (we treat this as a nuisance variable, essentially).

library(patchwork)

plot_percents <- function(percent_table){
  ggplot(percent_table, aes(y = percent, x = out_of, fill = source)) + 
    geom_col(position = 'stack') + 
    scale_fill_manual(breaks = c('ID', 'ID/Session', 'Other RE', 'Residual'),
                      values = apal[c(4,3,2,1)]) +
    scale_y_continuous(breaks = c(0, 20, 40, 60, 80, 100), labels = paste0(c(0, 20, 40, 60, 80, 100), '%')) + 
    labs(x = 'Variance (denominator)', y = '', fill = 'Variance source') +
    jftheme
}

plot_predictions <- function(amodel, point_alpha){
  adt <- as.data.table(amodel@frame)
  adt[, wave := factor(as.numeric(gsub('ses-(\\d+)', '\\1', sess)))]
  newdata <- unique(adt, by = c('id', 'sess', 'wave'))[, c('H', 'z') := list(0, NULL)]
  newdata$z_prime <- predict(amodel, newdata = newdata)
  newdata$z_prime_id <- predict(amodel, newdata = newdata, re.form = ~(1|id))
  ggplot(newdata, aes(x = wave, y = tanh(z_prime), group = id)) + 
    #geom_violin(data = adt, aes(group = NULL, y = tanh(z)), size = 0, alpha = .5, fill = apal[[1]]) +
    geom_point(data = adt, aes(group = NULL, y = tanh(z)), alpha = point_alpha, color = apal[[1]], position = position_jitter(), size = .5) +
    geom_point(color = apal[[3]], alpha = 1) + 
    geom_line(color = apal[[3]]) + 
    geom_rug(data = unique(newdata, by = 'id'), aes(y = z_prime_id, x = NULL), color = apal[[4]], alpha = 1, sides = 'tr', length = unit(0.03, "npc")) + 
    geom_hline(yintercept = 0, color = apal[[1]]) + 
    coord_cartesian(ylim = c(-.025, .65), xlim = c(1, 10)) + 
    labs(y = 'FC correlation', x = 'Session') + 
    jftheme
}

max_points <- unlist(sea_schaefer400_7_withinnet[, .N, by = net1][, list(max = max(N))])
point_alphas <- sea_schaefer400_7_withinnet[, .N, by = net1][, p := 1 - N / max_points][, pomp := (p - min(p)) / (max(p) - min(p))][, alpha := .025 + pomp*.1]

font_add_google("Didact Gothic", "Didact Gothic")
showtext_auto()
for(i in 1:length(model_fits)){
  model_fit <- model_fits[[i]]
  network_name <- networks[[i]]
  cat('\n\n### ', network_name, '{.tabset}\n\n') 
  cat('\n\n#### Plot\n\n')
  point_alpha <- point_alphas[net1 == network_name, alpha]
  print(plot_predictions(model_fit, point_alpha = point_alpha) + plot_percents(proportion_variance_tables[[i]]) +
          plot_layout(ncol = 2, widths = c(4,1)))
  cat('\n\n#### Table (%)\n\n')
  print(knitr::kable(tidyr::spread(proportion_variance_tables[[i]], out_of, percent), digits = 1))
  cat('\n\n#### Model Summary\n\n')
  cat('\n```\n')
  print(summary(model_fit))
  cat('\n```\n')
}

Cont

Plot

Table (%)

source	total	RE
ID	1.0	18.9
ID/Session	4.2	81.1
Residual	94.9	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: 43264.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.1502 -0.6815 -0.0690  0.6214  6.1069 

Random effects:
 Groups   Name        Variance  Std.Dev.
 sess:id  (Intercept) 0.0032216 0.05676 
 id       (Intercept) 0.0007512 0.02741 
 Residual             0.0734536 0.27102 
Number of obs: 186298, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept) 0.219396   0.006052   36.25

Default

Plot

Table (%)

source	total	RE
ID	0.0	0.2
ID/Session	3.8	99.8
Residual	96.2	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: 186542

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.8941 -0.6869 -0.0774  0.6111  6.0356 

Random effects:
 Groups   Name        Variance  Std.Dev.
 sess:id  (Intercept) 3.193e-03 0.056508
 id       (Intercept) 6.238e-06 0.002498
 Residual             8.027e-02 0.283317
Number of obs: 587200, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept) 0.219509   0.003376   65.03

DorsAttn

Plot

Table (%)

source	total	RE
ID	0.8	12
ID/Session	5.9	88
Residual	93.2	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: 58742.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.3597 -0.6952 -0.0868  0.6099  5.6408 

Random effects:
 Groups   Name        Variance  Std.Dev.
 sess:id  (Intercept) 0.0056105 0.07490 
 id       (Intercept) 0.0007634 0.02763 
 Residual             0.0879341 0.29654 
Number of obs: 141896, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept) 0.274478   0.006752   40.65

Limbic

Plot

Table (%)

source	total	RE
ID	2.8	27.1
ID/Session	7.5	72.9
Residual	89.7	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: -4379.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.4734 -0.6572 -0.0453  0.6094  5.7154 

Random effects:
 Groups   Name        Variance Std.Dev.
 sess:id  (Intercept) 0.004336 0.06585 
 id       (Intercept) 0.001615 0.04019 
 Residual             0.051994 0.22802 
Number of obs: 43652, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept) 0.195033   0.008373   23.29

SalVentAttn

Plot

Table (%)

source	total	RE
ID	0.3	5.5
ID/Session	5.8	94.5
Residual	93.8	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: 24325.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.1161 -0.6666 -0.0501  0.6035  6.4398 

Random effects:
 Groups   Name        Variance  Std.Dev.
 sess:id  (Intercept) 0.0042362 0.06509 
 id       (Intercept) 0.0002485 0.01576 
 Residual             0.0683081 0.26136 
Number of obs: 151093, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.26239    0.00484   54.22

SomMot

Plot

Table (%)

source	total	RE
ID	2.4	23.7
ID/Session	7.7	76.3
Residual	89.9	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: 98328.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-7.0465 -0.6703 -0.0996  0.5657  7.3652 

Random effects:
 Groups   Name        Variance Std.Dev.
 sess:id  (Intercept) 0.006352 0.07970 
 id       (Intercept) 0.001969 0.04437 
 Residual             0.074277 0.27254 
Number of obs: 407269, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept) 0.306326   0.009375   32.68

Vis

Plot

Table (%)

source	total	RE
ID	0.7	13.6
ID/Session	4.5	86.4
Residual	94.8	NA

Model Summary

Linear mixed model fit by REML ['lmerMod']
Formula: z ~ 1 + (1 | id/sess)
   Data: this_net_dt

REML criterion at convergence: 168003.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.5948 -0.7091 -0.0979  0.6330  4.8804 

Random effects:
 Groups   Name        Variance  Std.Dev.
 sess:id  (Intercept) 0.0053825 0.07337 
 id       (Intercept) 0.0008486 0.02913 
 Residual             0.1128402 0.33592 
Number of obs: 254358, groups:  sess:id, 289; id, 30

Fixed effects:
            Estimate Std. Error t value
(Intercept) 0.317526   0.006886   46.11